SOME NEW RESULTS ON WAITING TIME AND BUSY TIME IN M/G/1 QUEUE

This paper considers an M/G/1 queue with Poisson rate lambda > 0 and service time distribution G(t) which is supposed to have finite mean 1/mu. The following questions are first studied: (a) The closed bounds of the probability that waiting time is more than a fixed value; (b)The total busy time of the server, which including the distribution, probability that are more than a fixed value during a given time interval (0, t], and the expected value. Some new and important results are obtained by theories of the classes of life distributions and renewal process.

Waiting Time in Emergency Department in Riyadh 2017

Aim: To investigate the waiting times in the emergency department of both private and public hospitals. Methods: The study employs theoretical, qualitative, and quantitative approaches to come up with conclusions that are reliable. A total of 473 participants who had a direct interaction with the emergency department were asked to provide data on the waiting time, the kind of hospital they went to, the symptoms they had, and their gender for evaluation purposes. Common symptoms identified to the patients visiting the emergency department are related to head and neck, chest, abdominal pains, genitals, limbs, and back. It was found that more patients visited public hospitals over private hospitals. Additionally, more patients had symptoms related to abdominal than any other of the common symptoms and more males than females participated in the research. Data recording is done in tables using MS Excel and data presented through analysis using bar graphs for comparative purposes. Conclusion: Based on the results of the research, it was concluded that the efficiency of the emergency department is below the recommended standards. Finally, the recommendations made from the research findings included an audit of the emergency departments, increasing the staff in the department, and more research should be conducted throughout the country to come up with a more reliable record that is more inclusive.

Exact Distributions of Waiting Time Problems of Mixed Frequencies and Runs in Markov Dependent Trials

We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional γ slack cells without quotas. For any given and , in our Model I we determine the waiting time until at least frequency cells and at least run cells reach their quotas. For any given τ ≤ α + β, in our Model II we determine the waiting time until τ cells reach their quotas. Computer algorithms are developed to calculate the distributions, expectations and standard deviations of the waiting time random variables of the two models. Numerical results demonstrate the efficiency of the algorithms.

Emergency Department Waiting Times and Determinants of Prolonged Length of Stay in a Botswana Referral Hospital

Introduction: Emergency medicine is a critical component of quality public health service. In fact length of stay and waiting times in the Emergency department are key indicators of quality. The aim of this study was to determine waiting times and determinants of prolonged length of stay (LOS) in the Princess Marina Hospital Emergency Department. Methods: This was a retrospective observational study. It was done at Princess Marina, a referral hospital in Gaborone, Botswana. Triage forms of patients who presented between 19/11/ 2018 and 18/12/2018 were reviewed. Data from patient files was used to determine time duration from triage to being reviewed by a doctor, time duration from review by emergency doctor to patients’ disposition and the time duration from patient’s triage to disposition (length of stay). Prolonged length of stay was defined as duration > 6 hours. Results: A total of 1052 files repre- senting patients seen over a 1-month period were reviewed. 72.5% of the patients had a prolonged length of stay. The median emergency doctor waiting time was 4.5 hours (IQR 1.6 - 8.3 hours) and the maximum was 27.1 hours. The median length of stay in the emergency department was 9.6 hours (IQR 5.8 - 14.6 hours) and the maximum was 45.9 hours. Patient’s age (AOR 1.01), mental status (AOR 0.61), admission to internal medicine service (AOR 5.12) and pediatrics admissions (AOR 0.11) were significant predictors of prolonged length of stay in the emergency department. Conclusion: Princess Marina Hospital emergency department waiting times and length of stay are long. Age, normal mental status and internal medicine admission were independent predictors of prolonged stay (>6 hours). Admission to the pediatrics service was associated with shorter length of stay. There is a need for interventions to address the long waiting times and length of stay. Interventions should particularly focus on the identified predictors.

Waiting Times and Length of Stay of Trauma Patients in a Botswana Referral Hospital Emergency Department

Background: Mortality and morbidity due to trauma are a significant public health challenge. There is paucity of data on the waiting times and length of stay (LOS) of trauma patients in emergency departments in Botswana. The aim of this study was to determine the Emergency Department (ED) waiting times and LOS of trauma patients at Princess Marina Hospital in Gaborone, Botswana. Methods: This was a retrospective medical records review of waiting times (time from triage to review by ED medical officer) and LOS (time from triage to disposition from the emergency department). The waiting times for the different assigned acuities were assessed against the South African Triage System (SATS) standards. All trauma patients seen from 19/11/2018 to 18/12/2018 were included in the study. Prolonged length of stay was defined as duration > 6 hours. Categorical data was summarized with frequencies while numeric data was summarized with medians and interquartile ranges. Results: A total of 187 trauma patients’ files were analyzed. Of these, 72 (38.5%) were females. The median waiting time was 3.8 hours and the maximum was 19.2 hours. The median length of stay (LOS) was 8.8 hours with a maximum of 37.2 hours. Only 53 (28.3%) of the participants had a LOS of less than 6 hours. None of the emergent patients were seen immediately. Only 5 (4.0%) of the very urgent patients were seen within the target of 10 minutes. Finally, only 10 (20.4%) of urgent patients were seen within the target time of 1 hour. Conclusion: The waiting times and length of stay in Princess Marina Hospital were mostly above the recommended standards. Urgent interventions are needed to reduce waiting times and length of stay for trauma patients. More studies are needed to explore the sources of delay and investigate possible solutions to this public health challenge.

Waiting times and stopping probabilities for patterns in Markov chains

Suppose that C is a finite collection of patterns. Observe a Markov chain until one of the patterns in C occurs as a run. This time is denoted by τ. In this paper, we aim to give an easy way to calculate the mean waiting time E(τ) and the stopping probabilities P(τ = τA)with A ∈ C, where τA is the waiting time until the pattern A appears as a run.

VIRTUAL WAITING TIMES IN PRIORITY-M/G/1 QUEUES WITH VACARIONS

In this paper exhaustive-service priority-M/G/1 queueing systems with multiple vacations, single vacation and setup times are studied under the nonpreemptive and preemptive resume priority disciplines. For each of the six models analysed, the Laplace-Stieltjes transform of the virtual waiting time Wk(t) at time t of class k is derived by the method of collective marks. A sufficient condition for , where U has the standard normal distribution, is also given.

Analysis of Waiting Time in Emergency Department of Al-Noor Specialist Hospital, Makkah, Saudi Arabia

Emergency Department (ED) in Alnoor Hospital is considered the pulsating unit in the hospital by facing a daily challenge through a huge exposure to number of patients round between 500 - 700 per day in average. With this busy service in ED, our study emerges to measure the quality of provided services to patients in term of measuring the total length of stay time (LOS) in ED and its influencing factors. This is a prospective study aiming to estimate the average time patients spend in ED of Alnoor Hospital during the month of January (2013). In addition, it inspects factors influencing the LOS. The questionnaire which conducted and filled by emergency team over all patients was consisted of the following data: arrival time to ED, initial time of assessment by nurse, initial time of assessment by doctor, time of arrival to specific area, consultation time, arrival time of consulted specialty, time of laboratory investigation, time of radiological investigation, time of final disposition and time of physical disposition. For the 7604 patient visits analyzed, mean ED LOS was 3.02 hour (SD = 5.03 hour). About half of the patients spent less than 59 minutes (44%), 32.6% spent 1 to 3:59 hour, 15.2% spent 4 to 7:59 hour, and 8.2% of the patients spent more than 8 hours. A priceless such study will offer an opportunity to evaluate the recent ED performance and assist to adapt future optimization strategies to improve the quality of services provided to the patient.

Reaction Subdiffusion with Random Waiting Time Depending on the Preceding Jump Length

To describe the energy-dependent characteristics of the reaction-subdiffusion process, we analyze the simple reaction A--→B under subdiffsion with waiting time depending on the preceding jump length, and derive the corresponding master equations in the Fourier Laplace space for the distribution of A and B particles in a continuous time random walk scheme. Moreover, the generalizations of the reaction-diffusion equation for the Gaussian jump length with the probability density function of waiting time being quadratically dependent on the preceding jump length are obtained by applying the derived master equations.

Stochastic Model of Waiting Time: A Case of Two Selected Banks in the Sekondi-Takoradi Metropolis

Queue is an act of joining a line to be served and it is part of our everyday human involvement. The objectives of the study focused on using a mathematical model to determine the waiting time of two selected banks as well as compare the average waiting time between the banks. The study uncovered the extent of usage of queuing models in achieving customer satisfaction as well as permitting to make better decisions relating to potential waiting times for customers. The study adopted a case study and observational research with the source of data being primary. Purposive sampling technique was used to select the two banks under study with the target population comprising of all the customers who intended to transact businesses with the banks within the period of 11 am to 12 pm. The sample sizes for the first, second and third day of the first bank are twenty-eight (28), seventeen (17) and twenty (20) respectively with three servers on each day whereas that for the first, second and third day of the second bank is twenty (20), nine (9) and seventeen (17) with two servers on each day. A multiple server (M/M/s) Model was adopted, and Tora Software was the statistical tool used for the analysis. Findings of the study revealed that the second bank had a higher utilization factor than the first bank. Also, the number of customers in the banking hall of the second bank was higher than that of the first bank during the entire period of observation. Finally, it takes customers of the first bank lesser minutes to complete their transaction than the second bank. In conclusion, the three days observations revealed different banking situations faced by customers in both banks which had effect on waiting time of customer service. The waiting time of customer service has effect on the number of customers in the queue and system, the probability associated with the emptiness of the system and the utilization factor. Based on the results, the study recommended, inter alia, that the management of the second bank should adopt a three-server (M/M/3) model.

Bridging and downstaging treatments for hepatocellular carcinoma in patients on the waiting list for liver transplantation

Several therapeutic procedures have been proposed as bridging treatments for patients with hepatocellular carcinoma(HCC)awaiting liver transplantation(LT).The most used treatments include transarterial chemoembolization and radiofrequency ablation.Surgical resection has also been successfully used as a bridging procedure,and LT should be considered a rescue treatment in patients with previous HCC resection who experience tumor recurrence or post-treatment severe decompensation of liver function.The aims of bridging treatments include decreasing the waiting list dropout rate before transplantation,reducing HCC recurrence after transplantation,and improving post-transplant overall survival.To date,no data from prospective randomized studies are available;however,for HCC patients listed for LT within the Milan criteria,prolonging the waiting time over 6-12 mo is a risk factor for tumor spread.Bridging treatments are useful in containing tumor progression and decreasing dropout.Furthermore,the response to pre-LT treatments may represent a surrogate marker of tumor biological aggressiveness and could therefore be evaluated to prioritize HCC candidates for LT.Lastly,although a definitive conclusion can not be reached,the experiences reported to date suggest a positive impact of these treatments on both tumor recurrence and post-transplant patient survival.Advanced HCC may be downstaged to achieve and maintain the current conventional criteria for inclusion in the waiting list for LT.Recent studies have demonstrated that successfully downstaged patients can achieve a 5-year survival rate comparable to that of patients meeting the conventional criteria without requiring downstaging.

Application of a Quality Control Circle to Reduce the Wait Times between Continuous Surgeries

Purpose: To investigate how to shorten patient wait times between continuous ocular operations and to evaluate the influence of a quality control circle(QCC) on operating room management.Methods:.QCC management was established to conduct activities..Clinical data were collected to analyze the causes of long wait times between continuous surgeries. Effective measures were undertaken correspondingly.Results:.The staff from QCC actively undertook measures that would significantly shorten patient wait times between continuous ocular surgeries(P<0.05).Conclusion:.Multiple measures,.such as setting up a QCC,enhancing the arrangement of surgical procedures,.establishing effective communication channels,.optimizing human resources, and integrating the use of instruments, can effectively shorten patient wait times between continuous vitreous or retinal surgeries.

Scheduling a three-machine no-wait flowshop with separated setup time

In many practical flowshop production environments, there is no intermediate storage space available to keep partially completed jobs between any two machines. The workflow has to be continuous, implying that the no-wait conditions must be abided, which is typical in steel and plastic production. We discuss the three-machine no-wait flowshop scheduling problem where the setup times are considered as separated from processing times and sequence independent. The scheduling goal is to minimize the total flowtime. An optimal property and two heuristic algorithms for this problem are proposed. Evaluated over a large number of problems, the proposed heuristics are found that they can yield good solutions effectively with low computational complexity, and have more obvious advantage for the large size problem compared with the existing one.

Factors Determining Wait-Time and Patient Satisfaction at Post-Operative Orthopaedic Follow-Up

Introduction: There has been increasing attention on the evaluation of the efficiency and delivery of healthcare while trying to maintain the quality of service patients expect. A variety of studies have looked at various, non-orthopaedic surgical outpatient clinics and the factors involved in patient satisfaction and wait-time. The purpose of this study was to identify if such a relationship exist between the environmental, patient, and social-demographic factors to patient wait-time and satisfaction at an orthopaedic follow-up clinic. Methods: Patients were tracked through the clinic at various time points: appointment time, registration time, time to diagnostic imaging, time to being called into an exam room, time to being seen by a trainee, time to being seen by the staff surgeon, and time of leaving the clinic were collected. Overall satisfaction scores were calculated as per the VSQ-9. Patients who presented for their two or six week follow-up appointment were compared to those presenting for their three, six, or 12 month follow-up appointment. Result: A total of 80 patients were enrolled in this study. There was a good distribution of age and level of education. Ethnicity was heavily weighted towards the white population (76.6%) with the next largest ethnic group being East/Southeast Asian (7.8%). The mean total wait-time in clinic was 126.7 ± 46.5 minutes and the mean total VSQ-9 score was 78.5 ± 14.6. The longest time interval experienced by the patients in clinic was waiting for a consultation room after completion of imaging investigations (46.3 ± 33.3 min). The shortest time interval occurred once patients were in the consultation room and waited to be seen by the trainee or surgeon (15.0 ± 9.7 min. There were no statistically significant differences between the total wait-time in clinic, total VSQ-9 scores and age, gender, ethnicity, education, location of injury and overall health. Environmental variables were analyzed and it was found that patients reported greater satisfaction when seen only by the surgeon and not the trainee. Conclusion: Measurement variables have focused on patient satisfaction and wait-time as markers for improving healthcare. Although our study showed that there appears to be no association between any of the variables studied and wait-time or patient satisfaction, interventions at the patient level like using a custom designed clinic traffic flow board to track the position of each patient throughout their follow-up providing patients with a visual estimate of their position relative to other patients in queue may improve patient satisfaction and wait-time.

No-Wait Flowshops to Minimize Total Tardiness with Setup Times

The m-machine no-wait flowshop scheduling problem is addressed where setup times are treated as separate from processing times. The objective is to minimize total tardiness. Different dispatching rules have been investigated and three were found to be superior. Two heuristics, a simulated annealing (SA) and a genetic algorithm (GA), have been proposed by using the best performing dispatching rule as the initial solution for SA, and the three superior dispatching rules as part of the initial population for GA. Moreover, improved versions of SA and GA are proposed using an insertion algorithm. Extensive computational experiments reveal that the improved versions of SA and GA perform about 95% better than SA and GA. The improved version of GA outperforms the improved version of SA by about 3.5%.

Patron Survey of Acceptable Wait Times at Transit Bus Stops in the District of Columbia

The wait time of bus patrons at bus stops is one of several measures for assessing reliability of transit services, especially in urban areas. The uncertainty associated with waiting affects bus patrons’ perception of quali of the service provided. Studies in this subject area have therefore been of interest to transit service agencies and officials. This paper presents the findings of a study conducted to determine patrons’ maximum acceptable wait times (beyond the scheduled arrival time) at bus stops in an urban area. In all, 3387 bus patrons at 71 selected bus stops were surveyed over a period of 9 months. The results of the survey showed that the least acceptable wait time beyond the scheduled arrival time was 1 minute, while the maximum acceptable wait time was reported to be 20 minutes. Also, only one-third (33%) of the total number of patrons surveyed were willing to wait up to 5 minutes beyond the scheduled arrival time of buses. In addition, patrons are willing to wait longer in warm weather. On average, white patrons were found to have the least maximum acceptable wait times, followed by Hispanics, Asians, and then Blacks.

Risk Factors for Mortality of Patients Waiting for Elective Coronary Artery Bypass Graft Surgery

Background: Insufficient capacity for cardiac surgery results in extensive waiting time for patients requiring coronary artery bypass grafting (CABG). Previous studies have reported a consequence of an increased risk of mortality while waiting for CABG. Identification of risk factors for mortality is important in patients waiting for CABG. Objectives: To assess mortality rates and identify risk factors for mortality of patients waiting for CABG. Methods: This retrospective cohort study was done on patients waiting for elective CABG in dr. Kariadi General Hospital from January 2018 to December 2020. Identification of risk factors associated with mortality was done on patients who were waiting for CABG using logistic regression methods. Results: There were 162 patients fulfilling the criteria, with a mean waiting time for surgery of 9.8 months. While waiting for CABG surgery, 32 (19.7%) patients died of any cause. Independent risk factors for death while waiting for CABG included left ventricular ejection fraction ≤ 45% (OR 4.75;95% CI 1.76 - 12.78;p = 0.002), left main disease (OR 4.12;95% CI 1.50 - 11.27;p = 0.006), serum creatinine ≥ 1.5 mg/dl (OR 3.71;95% CI 1.41 - 9.74;p = 0.008), and a number of coronary artery disease risk factors ≥ 3 (OR 3.34;95% CI 1.24 - 8.99;p = 0.017). Conclusions: Long waiting time for CABG is associated with a high mortality rate which is influenced by left ventricular ejection fraction ≤ 45%, left main disease, serum creatinine ≥ 1.5 mg/dl, and a number of coronary arteries disease risk factors ≥ 3.

LSTM Based Spectrum Prediction for Real-Time Spectrum Access for IoT Applications

In the Internet of Things(IoT)scenario,many devices will communi-cate in the presence of the cellular network;the chances of availability of spec-trum will be very scary given the presence of large numbers of mobile users and large amounts of applications.Spectrum prediction is very encouraging for high traffic next-generation wireless networks,where devices/machines which are part of the Cognitive Radio Network(CRN)can predict the spectrum state prior to transmission to save their limited energy by avoiding unnecessarily sen-sing radio spectrum.Long short-term memory(LSTM)is employed to simulta-neously predict the Radio Spectrum State(RSS)for two-time slots,thereby allowing the secondary node to use the prediction result to transmit its information to achieve lower waiting time hence,enhanced performance capacity.A frame-work of spectral transmission based on the LSTM prediction is formulated,named as positive prediction and sensing-based spectrum access.The proposed scheme provides an average maximum waiting time gain of 2.88 ms.The proposed scheme provides 0.096 bps more capacity than a conventional energy detector.

急诊零停顿与急危重症患者一体化救治体系建设探讨

急危重症患者的救治体系是保障人民生命健康的关键环节,本文立足科技赋能,基于胸痛、卒中、创伤、危重孕产妇、危重儿童和新生儿急诊急救五大中心建设,提出急诊零停顿管理目标,从信息管理技术一体化、移动CT和移动卒中单元应用、院前急救即时超声应用、复合手术室应用以及新型急救技术及创新手术团队应用等方面探讨实现急诊零停顿的技术与措施,以提升急危重症患者的救治能力。